What Makes a Reaction Go Faster?

The rate of a reaction is how much reactant is used up, or how much product is made, each second Grade 10: Rate of chemical reaction. To measure it, you need something you can watch change: a gas given off, a color, a solid appearing, a mass falling.

Marble is calcium carbonate. Drop a few small marble chips into hydrochloric acid, and they fizz:
$$\text{CaCO}_3 + \text{2HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2$$
Lead the carbon dioxide into a gas syringe, and its plunger slides out as the gas fills it. Read the volume every 20 seconds and plot it against time.

The graph tells the whole story of the reaction:

• It is steepest at the start: the most gas comes off each second when there is the most marble to react.
• It gets less steep as the chips are used up.
• It goes flat when the reaction is over: here, when the marble has all gone (there was more acid than it needed). Both acids end with the same 48 mL, because the same chips made it.

The rate at any moment is the steepness, the gradient, of the curve: the rise in volume divided by the time it took. Over a stretch of time, that gives the average rate. The rate at one moment is the gradient of the tangent, a straight line that just touches the curve there. The rate at the very start, the initial rate, is the one chemists compare most, because at the start every run has the same amount of marble, and only the thing being tested is different.

Other reactions are timed in other ways: by the mass lost as a gas escapes from a flask on a balance, by a color fading (measured with a light meter), or by the time until something happens, as in the investigation at the end of this topic. A shorter time means a faster reaction, so the rate goes as 1 ÷ time.

Why should concentration matter at all? Because a reaction happens in collisions, and molecules collide far more often than you might think.

A nitrogen molecule in the air around you moves at about 500 m/s, faster than a passenger jet. It doesn’t get far: it hits another molecule after about 70 nanometers (70 millionths of a millimeter), and bounces off in a new direction. So each molecule collides about seven billion times every second.

If every collision made a reaction, every reaction between gases would be over in about a billionth of a second. The cooking gas and the air in your kitchen would have burned the moment they met. They don’t, because almost every collision is just a bump. For a collision to change the molecules, two things are needed:

1. Enough energy. The molecules must hit hard enough to start breaking their old bonds: with at least the activation energy, the hill on the energy diagram (Energy diagrams).
2. The right way round. Often the molecules must meet with the right parts touching, so that the atoms that will join can reach each other.

Together, these make collision theory: the rate of a reaction depends on how many collisions happen each second, and on what share of them are hard enough and the right way round.

Imagine one red molecule and one blue molecule in a box. Every so often they meet. Now put in a second red molecule. Each red one meets the blue one just as often as before, so there are twice as many red–blue collisions each second. Put in a second blue molecule as well, and each of the two red ones now meets two blue ones: four times as many collisions.

So the number of collisions between two kinds of molecule goes as the number of the first kind × the number of the second, in the same space. Try it.

The amount of a substance in each liter is its concentration, measured in moles per liter (mol/L). Doubling the concentration of one reactant doubles the number of its molecules in each liter, so it doubles the collisions with the other reactant each second. The share of collisions that are hard enough is the same as before (the temperature hasn’t changed), so twice as many collisions succeed each second, and the rate doubles. That is just what the marble chips showed: twice the acid concentration, twice the initial rate.

For gases, squeezing them into half the space doubles the concentration of every gas in the mixture. For a reaction between two gases, that is twice as many molecules of each, so about four times as many collisions between them each second.

The same idea explains surface area. In the marble reaction, the acid particles can only collide with the calcium carbonate on the surface of each chip. Crush the chips to powder, and much more of it is on a surface, so many more collisions happen each second Grade 10: Surface area.

When you warm something up, its molecules move faster. But temperature is only the average. In any gas or liquid, the molecules have all sorts of energies: they are always colliding and swapping energy, so at any moment a few are very slow, most have energies near the average, and a very few, by luck, are moving very fast. The way the energies are shared out was worked out by James Clerk Maxwell and Ludwig Boltzmann in the 1860s and 1870s.

For most reactions, the activation energy is far more than an average molecule has. Only the rare, fastest molecules, out in the tail of the distribution, have enough. And that tail is very sensitive to temperature: warm the molecules a little, and the hump of ordinary molecules hardly moves, but the number out in the far tail grows many times.

At 25 °C, only about 1 molecule in 110 million has 50 kJ/mol or more. Warm it to 35 °C, and the average energy rises by just 3%, while the number with enough energy nearly doubles. That is where the chemists’ rule of thumb comes from: near room temperature, many reactions go roughly twice as fast for every 10 °C warmer. (It is only a rough rule: a reaction with a higher activation energy is more sensitive to temperature, one with a lower activation energy less. For many reactions the factor is between about 2 and 3.)

So there are two reasons why a hotter reaction goes faster, and one matters far more than the other:

• The molecules move a little faster, so they collide a little more often: from 25 °C to 35 °C, about 2% more often.
• A much bigger share of the collisions are hard enough: from 25 °C to 35 °C, nearly twice as many.

Now the milk makes sense. Turning milk sour is the work of bacteria, and a bacterium is a bag of chemical reactions. Cool it from 35 °C to 4 °C, and the molecules lose only about 10% of their energy, but the share with enough energy to get over the hills of those reactions falls many times. The bacteria grow so slowly that the milk keeps for days.

You met catalysts in Grade 10 Grade 10: Catalyst: substances that speed a reaction up without being used up. Now you can see how much they can do. A catalyst gives the reaction a different path, with a lower hill. It doesn’t change the temperature, so the molecules’ energies are shared out just as before; but the line they must cross moves to the left, into the part of the tail where there are many more molecules.

In the widget, that would mean moving the red line from 50 kJ/mol to 40 kJ/mol. At 25 °C, that lets about 50 times as many molecules over. Enzymes, the catalysts in your body, often speed reactions up by millions of times, which is how your body can do at 37 °C what a laboratory would need strong acids and boiling to do.

Scientists explain a result in three parts: a claim (what is happening), the evidence (the measurements that show it), and the reasoning (the science that links the two). Collision theory gives the reasoning for every factor: count the collisions each second, and the share of them with enough energy.

• Why do some reactions get hot? Where the energy of a reaction comes from: breaking and making bonds, and the energy diagram with its hill.
• Why do some reactions stop halfway? Some reactions run both ways at once, each at its own rate. When the two rates are equal, the reaction seems to stop: how changing the conditions shifts the balance, as in making ammonia for fertilizer.
• How do you count atoms by weighing them? The mole, and how to work out how much a reaction makes.